SOLUTION: An airplane, flying with a tail wind, travels 1380 miles in 2 hours. The return trip, against the wind, takes 2.5 hours. Find the cruising speed of the plane and the speed of the

Question 681775: An airplane, flying with a tail wind, travels 1380 miles in 2 hours. The return trip, against the wind, takes 2.5 hours.
Find the cruising speed of the plane and the speed of the wind (assume that both rates are constant).
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Plane speed =x mph
wind speed =y mph
Against windx-y 2.5 hours
with wind x+y 2 hours

Distance = 1380 miles distance= 1380
t=d/r against wind
1380.00 / ( x - y )= 2.50

2.50 x - -2.50 y = 1380.00 ....................1
with wind x+y
1380.00 / ( x + y )= 2.00
2.00 ( x + y ) = 1380.00
2.00 x + 2.00 y = 1380.00 ...............2
Eliminate y in the linear system
Multiply (1) by 2.00
Multiply (2) by 2.50
we get y
5.00 x + -5.00 y = 2760.00
5.00 x + 5.00 = 3450.00
10.00 x = 6210.00
/ 10.00
x = 621 mph

plug value of x in (1) y
2.5 x -2.5 y = 1380
1552.5 -2.5 -1552.5 = 1380
-2.5 y = 1380
-2.5 y = -172.5 mph
y = 69
Plane 621 mph
wind 69 mph

CHECK
x+y= 690
X-y= 552 +
1380.00 / ( 690.00 )= 2
1380 / ( 552 ) = 2.5

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